BEIRUT, Lebanon — Thousands of people were sent fleeing for their lives on Monday as rebel fighters lost a large stretch of territory to government forces in the northern Syrian city of Aleppo, in what could prove to be a turning point in the conflict, both militarily and psychologically.

Residents described desperate scenes of people’s being killed by shells as they searched for shelter after their homes came under the heaviest bombardment yet of the nearly five-year civil war. Years of airstrikes and shelling have destroyed entire neighborhoods of the rebel-held half of the divided city, once Syria’s largest and an industrial hub.

At least 4,000 people have fled from the rebel-held eastern districts to the city’s government-controlled western side and have registered with the Syrian Arab Red Crescent in Jibreen, a neighborhood there, Jens Laerke, the spokesman for the United Nations office of humanitarian affairs, said on Monday.

As the rebels absorbed the harshest blow since they seized more than half the city four years ago, it seemed increasingly likely that President Bashar al-Assad would eventually manage to take back all of Aleppo.

That would give the Syrian government control of the country’s five largest cities and most of the more-populous west, leaving the rebel groups that are most focused on fighting Mr. Assad with only the northern province of Idlib and a few isolated pockets in the provinces of Aleppo and Homs and around the capital, Damascus.

Throughout the day, government troops, supported by Iranian-backed militias from Iraq and the militant group Hezbollah, advanced from the east and north into the rebel-held areas of Aleppo. That included Hanano, one of the first areas to fall, in 2012, and Sakhour.

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Residents of Aleppo, Syria, told us how they feel when they hear an aircraft overhead. Eastern Aleppo has been under heavy bombardment by Syrian and Russian forces.

Kurdish militias have staked out areas of de facto autonomy in parts of the country but are not entirely aligned with either the government or the rebels. The state news media and opposition activists have portrayed them in the current fighting in Aleppo, however, as working with the government to fight rebels. The Kurdish militias have clashed previously with rebels in Aleppo, who shelled the Sheikh Maksoud area.

If the government takes back the whole city, large parts of Syria will still remain outside its control, as Kurdish groups and the Islamic State hold most of the eastern half of the country. But it could effectively spell the end of the Syrian insurgent movements that sprang up against Mr. Assad after a crackdown on protests in 2011.

“It’s like doomsday,” said Zaher al-Zaher, an antigovernment activist in eastern Aleppo, who could communicate only in short bursts of text messages, as internet connections were failing.

Hisham al-Skeif, a member of a council in the rebel-held eastern districts of Aleppo, said he was scrambling to find housing for families who had fled from areas that had been recaptured by the government in the past day.

“The problem today, in this moment, is not water and food,” he said, at one point choking with tears. “We are threatened with slaughtering, slaughtering.”

The advances shattered a standoff that had lasted months, after government forces surrounded and besieged the rebel-controlled parts of the city this year, closing off regular access to food, medicine and other supplies.

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Pro-government forces in the Masaken Hanano district in eastern Aleppo, a day after they took it back from rebel fighters.CreditGeorge Ourfalian/Agence France-Presse — Getty Images

The battle of Aleppo has followed a pattern established by the government: Encircle a rebel-held area; bombard it with airstrikes, barrel bombs and artillery; hit not only rebels but medical clinics, schools and other civilian structures; and wait for exhausted residents to run away or make a deal.

That approach has worked in the old city of Homs, and in several Damascus suburbs. But eastern Aleppo is by far the biggest prize the government has tried to win in this way.

In the past two weeks of fighting alone, at least 225 civilians, including at least 25 children, have been killed by government bombardments in rebel-held areas. At least 27 civilians, including 11 children, have been killed by rebel shelling.

Despite an outcry from the United Nations and many governments condemning indiscriminate attacks, the world has largely stood by, unable or unwilling to stop the carnage, even as Syria’s civil war has become a proxy war, with Russia and Iran backing the government and the United States, Saudi Arabia, Turkey and others, to varying degrees, backing the rebels.

“This is violence that is organized and executed by the Assad government with the willing support of the Russians and the Iranians,” the White House press secretary, Josh Earnest, said Monday in response to the latest news from Aleppo.

The Syrian authorities and their allies made several offers to allow civilians and fighters to leave eastern Aleppo under government supervision, but there were few takers. People in eastern Aleppo said they did not trust the government to keep them safe, and government officials said the rebels were not allowing people to leave.

“We won’t have any mercy to those who confront the Syrian Arab Army,” one flier read, “but for those who will return to normal life, all the essentials of life will be secured.”

Another leaflet told rebels to abandon hopes that insurgents outside the city would break the siege.

“Don’t be dumb, think about yourselves and your families,” it read. “Victory is coming for the Syrian Arab Army, think quickly because time is passing and it’s not on your side.”

Some of the thousands who chose to flee on Monday headed for the Kurdish-controlled area of Sheikh Maksoud, where videos showed them scrambling over a berm; others went to government-held areas, where the state news media showed them thanking national leaders.

Others moved south into areas still controlled by rebels, only to find themselves still under bombardment. Modar Shekho, a nurse, fled his house with his brother, who was killed by a shell in the chaos. Their father, too, was killed as he looked for a gravesite, several of Mr. Shekho’s colleagues said.

Mr. Shekho’s friend Abdelkafi al-Hamdo, a teacher and activist, said in a text that Mr. Shekho would now have to choose between burying the dead, accepting condolences and looking for a house for his surviving relatives.